Possible Paper Topics. 1. The real case of the class number formula. We’ll be doing the imaginary case of this formula in class. I would definitely like someone to do this topic. Good sources include our textbook, and

Source URL: pages.iu.edu

DISTRIBUTION OF CLASS GROUPS OF QUADRATIC FIELDS AND RELATED TOPICS —A SURVEY— IWAO KIMURA (UNIVERSITY OF TOYAMA) Abstract. This is a survey talk on a distribution of ideal class groups of quadratic

Source URL: staff.miyakyo-u.ac.jp

• Algebra
• Abstract algebra
• Mathematics
• Algebraic number theory
• Quadratic forms
• Class number formula
• Complex multiplication
• Discriminant
• Main conjecture of Iwasawa theory
• Binary quadratic form
• Quadratic field
• Fundamental discriminant

615 Documenta Math. Kida’s Formula and Congruences To John Coates, for his 60th birthday

Source URL: www.math.uiuc.edu

• Algebraic number theory
• Galois theory
• Class field theory
• Field theory
• Cyclotomic fields
• Algebraic number field
• Main conjecture of Iwasawa theory
• Selmer group
• Iwasawa theory
• Galois module
• Splitting of prime ideals in Galois extensions
• Local class field theory

CLASSICAL AND ELLIPTIC POLYLOGARITHMS AND SPECIAL VALUES OF L-SERIES Don Zagier and Herbert Gangl1 The Dirichlet class number formula expresses the residue at s = 1 of the Dedekind zeta function ζF (s) of an arbitrary a

Source URL: people.mpim-bonn.mpg.de

Journal de Th´eorie des Nombres de Bordeaux), 293–307 Cryptography based on number fields with large regulator par Johannes BUCHMANN, Markus MAURER

Source URL: www.bmoeller.de

• Commutative algebra
• Ideals
• IP
• Commitment scheme
• Principal ideal
• Ln
• XTR
• Algebraic number field
• Class number formula
• Abstract algebra
• Algebra
• Algebraic number theory

A GROSS-ZAGIER FORMULA FOR QUATERNION ALGEBRAS OVER TOTALLY REAL FIELDS EYAL Z. GOREN & KRISTIN E. LAUTER Abstract. We prove a higher dimensional generalization of Gross and Zagier’s theorem on the factorization of dif

Source URL: eprint.iacr.org

• Number theory
• Modular arithmetic
• Analytic number theory
• Class field theory
• Symbol
• Artin reciprocity law
• Frobenius endomorphism
• Valuation
• Modular form
• Abstract algebra
• Mathematics
• Algebraic number theory

J OURNAL DE T HÉORIE DES N OMBRES DE B ORDEAUX A. M. O DLYZKO Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results

Source URL: archive.numdam.org

• Algebra
• Discriminant of an algebraic number field
• Riemann hypothesis
• Algebraic number field
• Discriminant
• Elliptic curve
• Upper and lower bounds
• Explicit formula
• Ideal class group
• Abstract algebra
• Mathematics
• Algebraic number theory

REAL QUADRATIC FIELDS WITH ABELIAN 2-CLASS FIELD TOWER ELLIOT BENJAMIN DEPARTMENT OF MATHEMATICS UNITY COLLEGE, UNITY, ME[removed]AND

Source URL: www.fen.bilkent.edu.tr

• Class number formula
• Quadratic field
• Discriminant
• Ideal class group
• Field extension
• Quaternion algebra
• Genus field
• Algebraic number field
• Class field theory
• Abstract algebra
• Algebra
• Algebraic number theory

IDEAL CLASS GROUPS OF CYCLOTOMIC NUMBER FIELDS I FRANZ LEMMERMEYER Abstract. Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefull

Source URL: www.fen.bilkent.edu.tr

• Class field theory
• Quadratic forms
• Field theory
• Conductor
• Class number formula
• Field extension
• Algebraic number field
• Tensor product of fields
• Signature
• Abstract algebra
• Algebra
• Algebraic number theory

KURODA’S CLASS NUMBER FORMULA FRANZ LEMMERMEYER Introduction Let k be a number field and K/k a V4 -extension, i.e., a normal extension with Gal(K/k) = V4 , where V4 is Klein’s four-group. K/k has three intermediate f

Source URL: www.fen.bilkent.edu.tr

• Symbol
• Field extension